No.
When you use Turbotax Online version, you can prepare only one return per account/payment. This Turbotax help topic tells you how to start another return:
https://ttlc.intuit.com/questions/1894512-how-do-i-start-a-second-return-in-turbotax-online
That is a fundamental difference between the Turbotax Online version, which you access through a web browser, and the CD/Desktop version which installs and runs on your home computer.
With the CD/Desktop version, you can prepare as many returns as you wish just for the price of the box.